Actors including Joanna Lumley, Sam West, Ralph Fiennes, Alan Rickman, Mark Rylance and Simon Callow have recorded video messages to David Cameron highlighting the plight of political prisoners held under the autocratic regime of the Belarusian dictator, Alexander Lukashenko.

The initiative has been organised by Natalia Kaliada and Nicolai Khazelin, co-founders of the Belarus Free Theatre, as part of the Free Belarus Now campaign and marks Wednesday's second anniversary of the rigged election that returned Lukashenko to power and a period when thousands of peaceful protesters were arrested.

"The regime does not want to show that there are any political prisoners," said Kaliada. "The authorities found different pretexts to make the arrests, things like hooliganism. Today there are still 14 political prisoners in jails of Belarus and they and their families are hostages of the last dictatorship of Europe."

The theatre company, as well as its artistic work, works to publicise the oppression that still goes on in Belarus. "They are a very brave gang of people," said long-term supporter Tom Stoppard.

The messages have been recorded by Lumley, Fiennes, West, Callow, Rylance, Rickman, Tim Rice and Adjoa Andoh. Fiennes highlights the cases of Zmitser Dashkevich and Pavel Seviarynets, who were detained in 2010 and are, according to Amnesty International, both prisoners of conscience.

Fiennes says: "Today, I appeal to David Cameron, prime minister of my country, to use the power of morality in politics, to disturb the sleep of conscience and urge Alexander Lukashenko, Europe's last dictator, to end the torture of his own people and release all political prisoners before the new year."

Despite the crackdown on the company, the Belarus Free Theatre continues to perform – at great personal danger and necessarily underground – in Belarus. Kaliada and her husband, Nicolai Khalezin, lead the company in exile and now live in the UK. In May, the company staged King Lear in Belarusian at Shakespeare's Globe to critical acclaim. Next year it will bring its new production, Trash Cuisine, to the Young Vic.

Stoppard said the situation in Belarus was bleak and there was more that the EU should be doing. "Democracies ought to be trying to make democracy contagious," he said, adding that he was full of admiration for the campaigners. "They are trying to remind the world at large that the Belarus problem hasn't gone away – it's got worse.

"The point is, what was true in the good old bad old days of communism is still true in the case of the Belarusian dictatorship. It is that publicity is definitely an inhibiting factor on people who would just like to have a free hand when it comes to thumping dissent on the back of the neck. Just the fact that this makes the news now and again is extremely important."

The initiative is about keeping the stories of unjustly persecuted people alive, giving moral support, he added. "It is about letting these people know that you haven't been filed away under 'oblivion'."

One year ago, an artists' manifesto for Belarus was published, calling for free speech and signed by Stoppard, Ai Weiwei and, in one of his last public acts, Václav Havel.

Irina Bogdanova, the director of Free Belarus Now, said of the new initiative: "I believe that sometimes what politicians can't do, people who genuinely care can. I hope that the voice of UK artistic elite will carry a strong message to the government and galvanize politicians into action.

"Messages coming from their hearts can't go unnoticed. I wish for a miracle to happen and for political prisoners to be with their loved ones for the new year celebration."

• This article was amended on 19 December 2012 to clarify details of the initiative highlighting the plight of political prisoners.